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DOI: 10.4230/LIPIcs.IPEC.2015.43
URN: urn:nbn:de:0030-drops-55703
URL: http://drops.dagstuhl.de/opus/volltexte/2015/5570/
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Barbero, Florian ; Gutin, Gregory ; Jones, Mark ; Sheng, Bin

Parameterized and Approximation Algorithms for the Load Coloring Problem

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Abstract

Let c, k be two positive integers. Given a graph G=(V,E), the c-Load Coloring problem asks whether there is a c-coloring varphi: V => [c] such that for every i in [c], there are at least k edges with both endvertices colored i. Gutin and Jones (IPL 2014) studied this problem with c=2. They showed 2-Load Coloring to be fixed-parameter tractable (FPT) with parameter k by obtaining a kernel with at most 7k vertices. In this paper, we extend the study to any fixed c by giving both a linear-vertex and a linear-edge kernel. In the particular case of c=2, we obtain a kernel with less than 4k vertices and less than 8k edges. These results imply that for any fixed c >= 2, c-Load Coloring is FPT and the optimization version of c-Load Coloring (where k is to be maximized) has an approximation algorithm with a constant ratio.

BibTeX - Entry

@InProceedings{barbero_et_al:LIPIcs:2015:5570,
  author =	{Florian Barbero and Gregory Gutin and Mark Jones and Bin Sheng},
  title =	{{Parameterized and Approximation Algorithms for the Load Coloring Problem}},
  booktitle =	{10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
  pages =	{43--54},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-92-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{43},
  editor =	{Thore Husfeldt and Iyad Kanj},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5570},
  URN =		{urn:nbn:de:0030-drops-55703},
  doi =		{10.4230/LIPIcs.IPEC.2015.43},
  annote =	{Keywords: Load Coloring, fixed-parameter tractability, kernelization}
}

Keywords: Load Coloring, fixed-parameter tractability, kernelization
Seminar: 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)
Issue Date: 2015
Date of publication: 09.11.2015


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